Question

What is a infinitely solution and two solution and unique solution in mathematics?

Answer 1

.. If one equation is a linear combination of two others then there is no unique solution. Here is an example 2x + y + z = 4, x - y = 0, 3x + z = 4. Not only is (1,1,1) a solution but also (2,2,-2) and (3,3,-7). In fact there are an infinity of solutions.

Answer 2

ANSWER

$Given equations are x+(a </p><p>2</p><p> −3a+3)y=a </p><p>2</p><p> and x+y=1</p><p>To have unique equations, </p><p>a </p><p>2</p><p> </p><p> </p><p>a </p><p>1</p><p> </p><p> </p><p> </p><p> </p><p></p><p> </p><p> = </p><p>b2</p><p>b1</p><p> </p><p> </p><p>where, a </p><p>1</p><p> </p><p> and a </p><p>2</p><p> </p><p> are X-coefficients</p><p>b </p><p>1</p><p> </p><p> and b </p><p>2</p><p> </p><p> are Y-coefficients of the given equations. </p><p>Therefore, </p><p>1</p><p>1</p><p> </p><p> </p><p></p><p> </p><p> =a </p><p>2</p><p> −3a+3</p><p>a </p><p>2</p><p> −3a+2 </p><p></p><p> </p><p> =0</p><p>a </p><p></p><p> </p><p> =2 or a </p><p></p><p> </p><p> =1$

The values of a∈R−{1,2} for the unique solutions.